Author | Deuflhard, Peter. author |
---|---|
Title | Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction / by Peter Deuflhard, Andreas Hohmann |
Imprint | New York, NY : Springer New York, 2003 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-0-387-21584-6 |
Descript | XVIII, 340 p. online resource |
1 Linear Systems -- 1.1 Solution of Triangular Systems -- 1.2 Gaussian Elimination -- 1.3 Pivoting Strategies and Iterative Refinement -- 1.4 Cholesky Decomposition for Symmetric Positive Definite Matrices -- Exercises -- 2 Error Analysis -- 2.1 Sources of Errors -- 2.2 Condition of Problems -- 2.3 Stability of Algorithms -- 2.4 Application to Linear Systems -- Exercises -- 3 Linear Least-Squares Problems -- 3.1 Least-Squares Method of Gauss -- 3.2 Orthogonalization Methods -- 3.3 Generalized Inverses -- Exercises -- 4 Nonlinear Systems and Least-Squares Problems -- 4.1 Fixed-Point Iterations -- 4.2 Newton Methods for Nonlinear Systems -- 4.3 Gauss-Newton Method for Nonlinear Least-Squares Problems -- 4.4 Nonlinear Systems Depending on Parameters -- Exercises -- 5 Linear Eigenvalue Problems -- 5.1 Condition of General Eigenvalue Problems -- 5.2 Power Method -- 5.3 QR-Algorithm for Symmetric Eigenvalue Problems -- 5.4 Singular Value Decomposition -- 5.5 Stochastic Eigenvalue Problems -- Exercises -- 6 Three-Term Recurrence Relations -- 6.1 Theoretical Background -- 6.2 Numerical Aspects -- 6.3 Adjoint Summation -- Exercises -- 7 Interpolation and Approximation -- 7.1 Classical Polynomial Interpolation -- 7.2 Trigonometric Interpolation -- 7.3 Bรฉzier Techniques -- 7.4 Splines -- Exercises -- 8 Large Symmetric Systems of Equations and Eigenvalue Problems -- 8.1 Classical Iteration Methods -- 8.2 Chebyshev Acceleration -- 8.3 Method of Conjugate Gradients -- 8.4 Preconditioning -- 8.5 Lanczos Methods -- Exercises -- 9 Definite Integrals -- 9.1 Quadrature Formulas -- 9.2 Newton-Cotes Formulas -- 9.3 Gauss-Christoffel Quadrature -- 9.4 Classical Romberg Quadrature -- 9.5 Adaptive Romberg Quadrature -- 9.6 Hard Integration Problems -- 9.7 Adaptive Multigrid Quadrature -- Exercises -- References -- Software